A new pressure-based lattice-Boltzmann method (HRR-p) is proposed for the simulation of flows for Mach numbers ranging from 0 to 1.5. Compatible with nearest-neighbor lattices (e.g., D3Q19), the model consists of a predictor step comparable to classical athermal lattice-Boltzmann methods, appended with a fully local and explicit correction step for the pressure. Energy conservation—for which the Hermitian quadrature is not accurate enough on such a lattice—is solved via a classical finite volume MUSCL-Hancock scheme based on the entropy equation. The Euler part of the model is then validated for the transport of three canonical modes (vortex, entropy, and acoustic propagation), while its diffusive/viscous properties are assessed via thermal Couette flow simulations. All results match the analytical solutions with very limited dissipation. Last, the robustness of the method is tested in a one-dimensional shock tube and a two-dimensional shock–vortex interaction.
A Lattice-Boltzmann model for low-Mach reactive flows is presented, built upon our recently published model (Comb & Flame, 196, 2018). The approach is hybrid and couples a Lattice-Boltzmann solver for the resolution of mass and momentum conservation and a finite difference solver for the energy and species conservation. Having lifted the constant thermodynamic and transport properties assumptions, the model presented now fully accounts for the classical reactive flow thermodynamic closure: each component is assigned NASA coefficients for calculating its thermodynamic properties. A temperature-dependent viscosity is considered, from which are deduced thermo-diffusive properties via specification of Prandtl and component-specific Schmidt numbers. Another major improvement from our previous contribution is the derivation of an advanced collision kernel compatible of multicomponent reactive flows stable in high shear flows. Validation is carried out first on premixed configurations, through simulation of the planar freely propagating flame, the growth of the associated Darrieus-Landau instability and three regimes of flame-vortex interaction. A double shear layer test case
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